Multi-antenna techniques can significantly increase the data rates and reliability of a wireless communication system. The performance is in particular improved if both the transmitter and the receiver are equipped with multiple antennas. This result in a multiple-input multiple-output (MIMO) communication channel and such systems and/or related techniques is commonly referred to as MIMO. A core component in mobile telecommunication networks of the 4th generation is the support of MIMO antenna deployments and MIMO related techniques.
An important aspect in the design of the transmission scheme is the peak to average power ratio (PAPR), which is a measure of how large the transmitted power peaks are in relation to the average power. (Although PAPR can be interpreted as a definition of a specific measure of the dynamics of a signal, PAPR is in this specification taken as a generic term that could map into several different forms of measures of dynamic range, including cubic metric.) The main problem with a large PAPR is that the transmitted signal should be within the, so called, linearity range of the power amplifiers (PAs). When the power peaks become too large, the PAs will cause clipping and/or other signal distortions that destroys the overall linearity of the effective propagation channel. Therefore, the PA design should be matched to the peaks of the transmitted signal. This is not so much of an issue in the downlink (DL) as in the uplink (UL), since the PAs at the radio base station, referred to as NodeB, do not suffer from the same cost, space, and power conception constraints as the PAs in the user equipment (UE).
To address the PAPR issue in the UL, the LTE standard has adopted single carrier frequency division multiple access (SC-FDMA), in favor of traditional orthogonal frequency division multiple access (OFDMA).
The SC-FDMA transmission scheme is illustrated in FIG. 1 and FIG. 4 for multi-antenna processing in the frequency domain (FD) and in the time domain (TD), respectively. Hence antenna ports 607 and a transmitter 606 are schematically illustrated. The case with frequency domain multi-antenna processing can be summarized as follows. First the information bit stream is encoded (e.g., using a turbo code) into one or several codewords that are mapped onto a sequence of N symbol vectors of modulation symbols, s(0), . . . , s(N−1). Each vector, s(k), has r elements, which corresponds to the transmission rank of the system; that is, how many data streams that are transmitted in parallel over the multi-antenna propagation channel. The main difference between SC-FDMA and OFDMA is that in SC-FDMA the symbol vectors belong to the time domain (TD), and are mapped to the frequency domain (FD), s0, . . . , sN−1, with a discrete Fourier transform (DFT) 140. The FD symbol vectors are next mapped onto N−1 different FD transmission symbol vectors, x0+k, . . . , xN−1+k, with a FD multi-antenna processing step 110, where k is the starting index of the allocation in the frequency domain. The symbols vectors, x0+k, . . . , xN−1+k, are mapped onto the consecutive sub-carriers, k, . . . , N−1+k, that have been allocated to the transmission. There is a one-to-one correspondence between the elements of xn and the antenna ports; that is, the lth element of xn corresponds to the signal of the nth sub-carrier on the lth antenna port. The FD transmission vectors are converted back to TD using an inverse fast Fourier transform (IFFT) 150 and application of a cyclic prefix (CP), into x(0), . . . , x(Nc+Ncp−1), were Nc is the number of sub-carriers and Ncp is the length of the cyclic prefix. Alternatively the multi-antenna processing of the signal can be performed in TD, as illustrated by FIG. 4, where the DFT is applied after the multi-antenna processing of the modulated symbols. It is also conceivable to have processing in both TD and FD.
The ambition with this SC-FDMA processing is that PAPR properties of the TD symbol vectors s(0), . . . , s(N−1) should be preserved in the transmitted symbol vectors x(0), . . . , x(Nc+Ncp−1). Given that the FD (and/or TD) processing step satisfies a number of constraints, the DFT operation (that differentiates OFDMA from SC-FDMA) ensures this PAPR relation. Since the symbol vectors s(0), . . . , s(N−1) are obtained using modulation constellations with limited peak powers, also x(0), . . . , x(Nc+Ncp−1) have limited peak power, which enables the use of cost effective relatively simple PAs.
The main problem with traditional SC-FDMA is the constraints it poses on the multi-antenna processing in the frequency domain (FD) and in the time domain (TD), since any of the following operations will significantly increase the PAPR of x(0), . . . , x(Nc+Ncp−1):
1. Linearly combining multiple elements of a FD symbol vector sk or a TD symbol vector s(t).
2. Most frequency selective processing; that is, processing that varies over the frequency band. An exception is a linear phase shift of all FD symbols, which corresponds to a simple cyclic shift of the symbols in the time-domain.
3. Rearranging the FD symbols; that is, make xk+m depend on other symbols than sm. For example, letting xk depend on s1 and xk+1 on s0, changes the frequency mapping of the symbols, which results in increased PAPR.
In single transmit antenna systems, these constraints are not particularly limiting. However, for MIMO systems these constraint pose sever limitations on the kind of processing that can be applied. For example, unconstrained frequency flat precoding, frequency selective precoding, as well as traditional space-frequency block coding (SFBC), all violate any of the above mentioned constraints 1.-3. which will result in an increase of the PAPR, as explained further below.
A straightforward solution for using more sophisticated multi-antenna processing is to ignore a PAPR increase and simply use sufficiently powerful PAs to handle the increased PAPR that is introduced by the FD multi-antenna processing. This approach suffers however from the obvious disadvantages of increased power consumption, increased heat dissipation, increased chip/radio-module size, and increased component cost.
In traditional frequency flat precoding, the FD symbol vectors, s0, . . . , sN−1, are mapped into the FD transmit symbol vectors, x0+k, . . . , xN−1+k, using a matrix multiplication as,xm+k=Wsm,where W is the precoding matrix. The frequency flat precoding can also be implemented in the TD as{tilde over (s)}(t)=Ws(t).
Unless there is explicit structure in W, each element in xm+k will be a linear combination of all the elements in sm (in case of TD precoding, {tilde over (s)}(t) is a linear combination of s(t)), which clearly violates at least the first of the above mentioned constraints on the FD and TD processing. To satisfy the constraints, each row of W can at most have a single non-zero element, corresponding to the single element in sm (or s(t)) that the antenna (of that row) depends on.
The reduced degrees of freedom in the design of such a PAPR friendly precoder W will however penalize the efficiency of the MIMO processing, and thus also the MIMO gain of the link.
In wideband frequency allocations the effective propagation channel can change significantly over the sub-carriers. To match the varying channel, the precoder matrix should be adapted accordingly to provide frequency selective precoding, resulting in the following mappingxm+k==Wmsm,where the precoder Wm may be different for each sub-carrier. However, even if each precoder matrix only has a single non-zero element per row, as mentioned above, the frequency selectivity clearly violates the constraints for preserved PAPR properties.
Space Frequency Block Coding (SFBC) is the working assumption for downlink open-loop rank one transmission (only a single data stream is transmitted in parallel) in the 3GPP LTE specifications. In case of two transmit antennas, pairs of FD symbols, (s2n,ssn+1), are encoded jointly to form a pair of FD transmit symbol vectors (xk+2n,xk+2n+1) using the classical Alamouti mapping:
            x              k        +                  2          ⁢          n                      =          [                                                  s                              2                ⁢                n                                                                                        s                                                2                  ⁢                  n                                +                1                            c                                          ]        ,            and      ⁢                          ⁢              x                  k          +                      2            ⁢            n                    +          1                      =                  [                                                            s                                                      2                    ⁢                    n                                    +                  1                                                                                                        -                                  s                                      2                    ⁢                    n                                    c                                                                    ]            .      This encoding schemes violate constraints (the above mentioned constraint 3.) for preserving the low PAPR; the second antenna rearranges the symbol dependence; that is, [xk+2n]2 depends on s2n+1, and [xk+2n+1]2 depends on s2n (where [x]m denotes the mth element of the vector x). Hence, the coding scheme does not satisfy the constraints for preserving the PAPR relation for all antennas.